Can I set up one background image per scene?
Background images are part of UI data, that means they are saved along with user interface information withing the blend file, as such they cannot be different per scene, because UI data is saved once per file only.

As a side note you can also notice that if you disable the Load UI option when opening a file, background images will be gone.

They can still be controlled on a per-viewport basis, though, so two different 3D scene views can have different visible images, but the list will show the same datablocks.

Blender 2.8 post production effects and settings will probably be part of scene or even layer data, as such they have nothing to do with background image settings and can be independent per scene, as far as I know. Nothing is written in stone yet.

You could try using Empty objects as images as an alternative.